Wet and dry starting with a 1500 grade, working up to a 2500 grade, followed by a machine polish with a cutting compound will sort it out. They will need a sealant afterwards and that maintained regularly.
It's the anti-UV protective coating that breaks down and goes cloudy. Once you've taken that off, there is no UV protection, so the polycarbonate lenses will go all cloudy. It's a vicious circle.